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Derivative of lg^2(x-2)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2       
log (x - 2)
$$\log{\left(x - 2 \right)}^{2}$$
log(x - 2)^2
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Let .

    2. The derivative of is .

    3. Then, apply the chain rule. Multiply by :

      1. Differentiate term by term:

        1. Apply the power rule: goes to

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
2*log(x - 2)
------------
   x - 2    
$$\frac{2 \log{\left(x - 2 \right)}}{x - 2}$$
The second derivative [src]
2*(1 - log(-2 + x))
-------------------
             2     
     (-2 + x)      
$$\frac{2 \left(1 - \log{\left(x - 2 \right)}\right)}{\left(x - 2\right)^{2}}$$
The third derivative [src]
2*(-3 + 2*log(-2 + x))
----------------------
              3       
      (-2 + x)        
$$\frac{2 \left(2 \log{\left(x - 2 \right)} - 3\right)}{\left(x - 2\right)^{3}}$$